Like other technical staff members in the theory department, I occasionally passed computational tasks to a math and computation group in GMRD. On several occasions, I was amazed by the response. Contrary to my previous experience with such groups, where the results provided were technically correct but not very useful for the physical problem involved, these solutions were just what was needed for the application. After this had happened a few times, I asked who in the mathematics group had been responsible for this work and discovered that it was none other than Glen, who had left UCB and come to work for TRW. We promptly invited Glen to join our Aeronautical Research Lab as a house mathematician and over the next several years he and I had some enjoyable collaborations, one of which led to a publication on gravity turns which I still consider a pretty piece of work. (Then, and for some years thereafter, I continued to be impressed and surprised by Glen's uncanny ability to not only solve mathematical problems which had arisen from some physical application but to produce solutions of just such a character as to be most useful for the application which had led to the mathematical problem. I supposed that Glen must have a stronger background in physics than I had realized, so that, given a mathematical problem, he deduced what physical problem had generated it and used the physics as a guide in solving the mathematical problem. Eventually, I realized that hypothesis was dead wrong: Glen's knowledge of physics was limited, but he had a superb geometric intuition. Given a mathematical problem, he found a geometric analogue and used that to guide his problem-solving strategy, rather than the relevant physics.)
After a few years at RW, Glen decided to go back to graduate school, at UCLA, where he was accepted as a student by Magnes Hestenes, a world-class mathematician, known especially for his work on Calculus of Variations. Glen's thesis was an impressive piece of work, and Prof. Hestenes thought so highly of Glen in general that he assured Glen he could get him a faculty appointment in any math department in the country -- Glen had only to name his preference. In what seemed to some a surprising choice, Glen picked UCSB. I imagine that he must have (correctly) perceived that this, then small and not yet very famous, campus was a place where he would be relatively free to develop his own ideas, without the pressures and politics of larger, more prestigious departments.
During the period from 1954 to 1960, RW merged with Thompson Products (an old line Cleveland manufacturer of airplane and automobile engine valves, etc., which had provided the original funding for Si and Dean to set up RW) to become the Thompson Ramo Wooldridge Corp. (later shortened to TRW). GMRD, which had experienced a very rapid growth, was spun off as a wholly owned subsidiary of TRW, called Space Technology Laboratories (STL), and the RW Computer Division moved to a campus-like research park which TRW had established on Fallbrook Ave. in Canoga Park, where Si Ramo spent much of his time. A true visionary, he saw more clearly than most others at that time how our society would be transformed by the computer and the opportunities this would provide for high technology companies; his only error, I believe, was that, characteristically optimistic, he underestimated the time it would take for the developments he foresaw to be realized. He had coined the term "intellectronics" to describe this field and in 1960 he decided to establish an "Intellectronics Research Laboratory" in the Canoga Park operation. In the spring of that year, he asked me to organize, and serve as director of, such a research lab.
While I was, of course, very pleased to receive such an offer, I had some qualms about accepting it. I had no hands-on computer experience, having never even written a line of Fortran. When I needed computational work in the course of my work as a theoretical physicist, I relied on some programmer to take my equations and provide numerical solutions. A few days later, when Glen came down to consult at STL, I told him of about Si's offer and my reservations. He thought it was a marvelous opportunity, to which I replied that it certainly would be for him, with his computational background and abilities, but I felt ill prepared for the job. We discussed it for awhile and then Glen proposed a (characteristically creative) resolution. If I took on the directorship of the new lab, he would take a year's leave from UCSB to come down and work with me. Having profound respect for Glen and his abilities, I recognized this as an opportunity not to be missed, so I accepted Si's offer; Glen took leave from UCSB; and by the summer of 1960 the new lab was in operation, with a number of outstanding scientists as consultants to help choose directions and programs.
During the preceding several years, the RW Computer Division had designed and built, under a contract from the Air Force's Rome (New York, not Italy) Air Development Center (RADC) a computer, called the RW400, which was very advanced for that era. Designed for Command and Control applications, it was a modular computer, comprised of a number of different hardware elements which could be interconnected in various ways using a large, computer controlled, electronic switch. The elements included a CPU; two buffers; two magnetic drums, one small and one large; and magnetic tapes. The most important feature was a very sexy console (or terminal, in modern terms) with two keyboards; a very large CRT with graphic capabilities, including cross hairs and a light pen for direct, on-screen graphic input; and a smaller CRT with hardware for displaying alpha-numeric information. Two RW 400's had been built, one which was shipped off to RADC and one which remained in Canoga Park for further testing and development. As soon as Glen saw the RW400 and understood its hardware capabilities, he said softly, and with his characteristic smile, "We could do some interesting things with that." As usual, he was completely correct.
It must be remembered that in 1960 (and for many years thereafter) virtually the only means of communication with the large computers used for complex physical problems was via punched cards (for input) and numerical print-outs, for output. The computational solution of a complex physical problem involved a number of serial steps: 0) make such approximations to the physics as might be necessary to obtain a reasonable set of mathematical equations; 1) find an algorithm for constructing a numerical solution to these equations; 2) make appropriate choices for relevant parameters, e.g., step size in integration routines; 3) write a program, in Fortran or some other "higher" language; 4) convert the program to punched cards; 5) feed the cards into the computer; and 6) after some time -- minutes, hours, or even days, depending on the size of the problem and the length of the computer queue -- get back a printout, consisting of lists of numbers, which could be graphed, when appropriate. Given that unwieldy process, experimentation -- with the physical approximations; with the choice of algorithm; with the parameters; etc. -- was scarcely feasible. Glen, intimately familiar with this traditional "batch" method, had given much thought to a totally different approach to the computational solution of such problems. He envisioned a system which would allow such close interaction between user and computer as to allow a truly experimental approach to problem solving -- in short, what we now call interactive computing (although the word "interactive" was not then used in that context). Upon seeing the RW400, he immediately perceived that this was a hardware facility on which he could realize and try out some of his ideas.
The first step was to try the new approach on some suitably difficult problem. We felt strongly that this should not be simply a "demonstration problem," i.e. one which had previously been solved by conventional techniques, but rather a new problem, of sufficient interest that its solution would be of value in itself, regardless of the method of solution. One of the summer consultants was Bob Schrieffer, a talented theoretical physicist who, in collaboration with John Bardeen and Leon Cooper, had recently published a new theory of superconductivity, based on first principles, which soon became known as the BCS theory (and subsequently earned them a Nobel Prize). To obtain quantitative results from the theory, it was necessary to solve a moderately complicated nonlinear integral equation. They had obtained good agreement with experiment by solving the equation using a rather crude approximation (that the "energy gap," G, a critical element of the theory, was independent of the energy, E), but Bob was interested in exploring the consequences of a more sophisticated approach, in which the energy gap is a function of energy, G(E), this function being obtained by solving the aforesaid integral equation. This seemed like a good initial problem on which to test Glen's ideas (and the capabilities of the RW400), so Glen and Bob Huff, another one of the summer consultants (a theoretical physicist by training, but with exceptional programming skills) set about programming the RW400 to solve the BCS integral equation. (This programming task was monumental since the RW400 had no higher language of any sort; programming had to be done in 28 bit machine language!)
What Glen and Bob Huff did was to program the essential macros needed for the problem (forerunners of the "console programs" of Glen's subsequent On-line Mathematical Systems), assigning each one to a key of the RW400 left hand keyboard, so that users, like Bob Schrieffer or me, could sit at the key board and experimentally seek solutions of the integral equation. (Functions, represented by 101 component vectors, could be "stored under" the keys of the right hand keyboard or in a vector accumulator. Operations on these functions, e.g. convolution with the kernel of an integral equation, arithmetic or algebraic transformations of a function, graphic display of a function, etc. could be called by simply pressing the appropriate key of the lefthand keyboard. A curve, displayed in the CRT, could be modified by use of the light pen or crosshairs.)
With this capability, it was quite feasible, to sit at the console and vary G(E) (by mathematical transformations or by manipulation of portions of the graphically displayed curve of G vs. E using the light pen and crosshairs) until it satisfied the integral equation. For example, if an integral equation has the form K#G=G, where K represents the kernel and # denotes convolution, one approach is straightforward iteration: generate a sequence of functions G, G,..... where G[n+1] = K#G[n]. Starting with some G, the sequence will, in some case (but by NO means all!) converge to the solution G of the integral equation. By generating and then graphically displaying subsequent functions in the sequence, one can quickly see whether the sequence converges and, if it does, when the difference max|G[n+1] - G[n]| is small enough so that G[n] is an adequate approximation to G. If it does not converge, one can see whether the divergence is oscillatory or exponential in character and from that derive strategies for more sophisticated methods of solution. Since the iteration failed to converge for the most interesting parameter values and since the BCS equation was nonlinear, rather than linear, as in this example, obtaining physically significant results was still far from easy.
Needless to say, using this capability provided as much fun and excitement as any good adult toy. The Computer Division engineers needed the RW400 for testing during the day, leaving the machine for us to use at night. I have vivid memories of working with Glen at the console until the wee hours of the morning, and coming out of the building into the clear night air feeling elated and exuberant. We were solving a difficult problem using an approach which was, as far as we knew, unique in the world. (Sally still has equally vivid memories of my frequently arriving home in Pacific Palisades at 3 a.m., after negotiating the challenging topography of Topanga Canyon Blvd.) Our enthusiasm was tempered somewhat by some sense of frustration, because it was virtually impossible to tell anyone else what we were doing: it was so at variance with the standard approaches and capabilities with which people were familiar that it was exceedingly difficult to explain to others.
Our test of the validity and power of Glen's concepts was an outstanding success. We obtained physically interesting results for the BCS theory and (with Bob Schrieffer) published them in Physical Review. Unbeknown to us, a group at one of the IBM laboratories, had attacked the same problem, using a large IBM computer (whose number crunching capabilities dwarfed those of the RW400), but with a conventional batch approach. Their paper appeared at about the same time as ours, but because they lacked the capability for experimental problem solving, they had to make some additional simplifications and approximations to the physics, with the result that their G(E) solutions lacked some of the structure which ours exhibited and which was essential in obtaining good agreement between the predictions of the BCS theory and the experimental results on one class of superconductors.
Even more important, it was now clear (to Glen) how to generalize from this one problem to a large part of mathematical physics. Instead of programming the macros for a specific problem, as had been done in solving the BCS equation, one should program the fundamental operators of algebra, trigonometry and calculus, together with a simple on-line procedure for combining them into the macros needed for any specific problem and a simple, but general graphical display capability.
Glen took an extra year's leave of absence from UCSB and, together with a young programmer named George Boyd, implemented on the RW400 the first version of the interactive On-line Mathematical system. Some of our consultants returned during the summer of 1961, used the system, critiqued it, and came up with suggestions which Glen considered carefully in designing the next version. In any such system, there are many decisions on just which operations to include in the basic set, how much redundancy is appropriate, etc. For example, if the basic set includes EXP and LOG, it is clearly redundant to include SQ and SQ ROOT, yet experience shows that it is wise to do so. A combination of Glen's good judgment and our increasing experience with use of the system provided the basis for these decisions, some of which were modified in later implementations, as more problems were solved using the system, providing an increasing basis of experience.
Dick Feynman, who came over from Cal Tech occasionally, had some vigorous discussions with Glen regarding the choice of mathematical syntax. John Ward, a well known, brilliant, and somewhat eccentric elementary particle physicist liked to experiment with the system but insisted on two conditions: that George Boyd be in the room when he was running, in case he encountered any difficulties, but that George must sit with his back to John, who didn't want to be watched while using the terminal. Bob Schrieffer pointed out the lack of one rather fundamental operation: evaluation of a function (numerically represented by two associated vectors) at a given value of the argument. I think Glen may have been a trifle embarrassed by this omission, since his response was to provide a much more generalized (and valuable) version of what Bob had requested: an operator called EVALUATE . Given three vectors z, x and y with the values in y lying between the maximum and minimum values of x, this operator generates a new vector w, whose values are obtained by linear interpolation on the values of z according to the following rule: let z and x represent a function f, via z = f(x). Then w gives the values of the function f at the points of y. If y is a constant vector, this gives evaluation of f(x) at one point. More generally, we obtain values of f at new values (namely y, y, etc) of the independent variable. (Combined with the REFLECT operator this gives a simple and powerful way of accurately inverting a numerically specified function.)
By the fall of 1962, Glen had returned to UCSB and begun to set up his famous on-line classroom and I had decided to return to research in plasma physics, first back at STL, and then, starting in 1963, at UCLA , as a professor in the Physics Department. Two RW engineers who had been most helpful to us, Roland Bryan and Truett Thach, left RW and went to work at the west coast division of Bolt, Beranek and Newman, a venerable east coast acoustics company which was getting into electronics and computing. They and Glen persuaded a BBN vice-president, Bill Galloway, that BBN should manufacture the teleputer, a terminal designed for the on-line system by Glen and Roland. It consisted of a dedicated keyboard; a very small (5") Tektronix storage oscilloscope, which greatly reduced the computer hardware required to drive graphical displays; and the associated electronics, which for a four terminal system, occupied two cabinets, each the size of a bar refrigerator! (To get hard copy graphic output, it was necessary to take a polaroid snapshot of the Tektronix screen and then coat the print with a plastic gel contained in a felt applicator supplied with each pack of polaroid film. We all went around with the smell of the solvent used in those applicators clinging to our hands.)
The teleputers were used by Glen in his classroom and also at STL, where I was working part time and Glen was still a consultant. A number of the STL engineers and scientists were impressed by the capabilities of the On-line Mathematical System and we were able to secure the funding required to set up a four station version at STL. In addition to the teleputers, it used a computer designed for process control applications, the Bunker-Ramo 340. Under Glen's detailed supervision, a group of 3 or 4 STL programmers created another implementation of the On-line Mathematical System, essentially similar to the final RW400 version, but with a few improvements suggested by our increasing experience in using the system for solving a variety of problems. It operated at STL for several years and saw considerable use by those technical staff members who were not too steeped in conventional computing to accept this new technique. (Economic necessity dictated that this be a multi-user system, and hence that the problem of time-sharing be solved, along with the implementation of the online system itself. The RW400 had been a "free" computer, so there was no difficulty in its being a single user facility, but even a relatively small computer like the Bunker-Ramo 340 was too expensive too be appropriate for single user operation. Glen's criterion was that the hourly cost per station be approximately equal to the hourly wages of the person using it.)
During the mid-sixties, Glen and I published some papers describing this new approach to computational problem solving and presented similar material at several conferences. However, it continued to be difficult to get the ideas across to people whose only experience with computing was the conventional batch mode approach or those for whom Fortran and computing were synonymous. This was forcibly brought home to us during a visit to California by Tony Oettinger, a very sharp, highly respected MIT computer scientist. At that time, the STL on-line system was in operation, but Glen was between systems at UCSB and did not have a version up and running. Tony visited Glen in Santa Barbara, listened carefully to his description of the on-line systems, understood what he heard, and came away very favorably impressed. The next day, he visited me in L.A. and I sat down with him at one of the STL terminals to demonstrate the system. I had only pushed a few keys [ID DISPLAY RETURN (which generated the "identity function," y = x, and plotted it on the scope)] when Tony jumped up in excitement -- I could almost see a light bulb going on above his head, cartoon fashion -- and shouted "NOW I understand!!". He had comprehended Glen's description in some intellectual sense, but only when he saw the actual implementation did he really grasp the essence of this new technique.
This and other experiences convinced us that presentations should include live demonstrations whenever possible, something which was not easy to accomplish given the technology of that era. On one memorable occasion, we presented a paper at a WESCON meeting in San Francisco before an audience of several thousand people. Roland and Truett arranged for the shipment of two teleputer terminals to San Francisco, the installation of a modem and a "conditioned" telephone line to UCSB, and a closed circuit TV projection system with a camera trained on one teleputer scope, the image being projected on a huge screen, clearly visible to the whole audience. Glen asked me to make the presentation, while he stayed in Santa Barbara to baby sit the computer. Along with the other 3 speakers for that session, I was seated on the stage at a table which held a keyboard and a small Tektronix storage scope (the camera being trained on a second, slaved scope.) A partition at the front edge of the table made it possible for me to use the keyboard and watch the scope, out of sight of the audience. During the two talks preceding mine, I kept playing with the system, getting a nice, warm feeling from the fact that it was working perfectly. When my turn to speak came, I carried the keyboard, which was on a long cable, to the podium. and launched into a description of the system and some illustrations of using it to solve problems.
I had been talking only a few minutes when, to my horror, the telephone attached to the modem (which was sitting at the back of the stage) began to ring. I assumed that it must be Glen calling, and since he knew that I had started the talk, he must have something absolutely critical to tell us. "Roland," I said into the microphone, "could SOMEONE please answer that!". This was a catastrophic error on my part for when Truett picked up the phone there was no one on the line -- but the computer connection was broken! When Truett tried to phone Glen on that line, he could only get a busy signal, since Glen (who, it turned out, had not been calling us) had no way of knowing our situation. With considerable egg on my face, I fell back on the weak expedient of describing to the audience what they would be seeing on the screen at each point, if the system were operational. Shortly before the end of my allotted time, Roland and Truett somehow got things working again, but it was a traumatic experience for all of us. (Later, Roland discovered that the ringing had been triggered by some of the walkie-talkies used by the security or conference personnel on duty in the auditorium. Had I had the wit to ignore the ringing, all would have been well.)
During the next two decades, several more versions of the system were implemented, each with improvements and refinements based on experience and made possible by the rapid advance of computer hardware capability. When Glen got his classroom system up and operational, the plasma theory group at UCLA purchased several teleputers and Glen provided us with access to the system via telephone line. This was very helpful, but continual troubles with the telephone line made it advisable to implement the system on the UCLA IBM 7090. Glen was too busy exploiting new ideas to again come to L.A. and supervise a group of programmers, so we assigned to three UCLA computer center programmers the non-trivial task of implementing on UCLA's IBM 7090 computer a system which would look to the user the same as Glen's UCSB system. The IBM machine was not designed for interactive use and differed so much from the RW400 and the Bunker-Ramo 340 that the programs of those computers were in no way transferable. The UCLA programmers had to start from scratch, and every time they pronounced the assignment impossible and were ready to give up, I would lead them to one of the terminals connected to the UCSB system and say, in effect: "Here's the proof that what we're asking for is possible; I'm sure you guys are clever enough to figure it out how to do it." Somehow it worked, and the group (one of whose members, Bill Drain, later became Director of the UCLA computing center, the Office of Academic Computing [OAC]) produced a very nice version of the system, using as consoles the larger Tektronix storage scope terminals which had by then become available.
A few years later, John Dawson, the leading pioneer in the field of computer simulation of plasmas, joined the UCLA Physics Dept. He and Glen had a very fruitful interaction, resulting in our purchasing from Culler Harrison a CHI computer which provided both an advanced and powerful version of the On-line Mathematical System and a facility for carrying out plasma computer simulations which competed favorably with the largest computers (the Cray) then being used by other groups for such studies. By the 1980's, when the CHI system suffered some irremediable hardware failure, personal computers had become so powerful and inexpensive that it was economically feasible to have a single user on-line system. At the same time, it was clear that in addition to its value as a problem solving tool, it would be valuable to have the On-line Mathematical system available on a large facility like the National Magnetic Fusion Computer Center Crays at LLNL for use as a post-processing tool. With financial support from LLNL, one of the UCLA plasma theory research physicists, Robert Ferraro, implemented (in a combination of C and Fortran) a version of the system which was essentially machine-invariant and which has been running on PC's, Macs, the IBM 360 at UCLA's Office of Academic Computing and the NMFCC Crays.
Over a period of two decades, these various versions of the on-line system gave our plasma theory group a very significant edge over others in the field. They were a critical resource for many of the papers we published and for a number of PhD dissertations by students working with John Dawson, George Morales, me, and others. Glen, too, made good use of his online systems, not only for teaching but also for seminal investigations of human speech structure needed for his work on analysis and synthesis of speech.
Looking back on more than thirty years of active involvement with Glen as collaborators, colleagues and friends I realize how stimulating and enjoyable it has been, thanks to his remarkable creativity, his gentle manner, his unfailing good humor, his enthusiasm, his positive outlook, and his sensitivity and genuine concern for everyone with whom he works. I am also conscious of how much I have learned from Glen. Since I left graduate school, the two people who have most profoundly affected my understanding of the analytic and computational aspects of physics were both mathematicians: the late Karl Menger, a world-class topologist and mathematical philospher, whose friendship I was privileged to enjoy over some 40 years, and Glen Culler. I consider Glen to be one of the most creative people I have known during my career and it is a real pleasure to see him receiving now the recognition which he so thoroughly deserves.